Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of Second Order
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Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of Second Order
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Author : A. V. Ivanov
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of Second Order written by A. V. Ivanov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of The Second Order
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Author : A. V. Ivanov
language : en
Publisher:
Release Date : 1984
Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of The Second Order written by A. V. Ivanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
Theoretical And Mathematical Physics
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Author : Vasiliĭ Sergeevich Vladimirov
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Theoretical And Mathematical Physics written by Vasiliĭ Sergeevich Vladimirov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Linear And Quasi Linear Equations Of Parabolic Type
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Author : Olʹga A. Ladyženskaja
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Linear And Quasi Linear Equations Of Parabolic Type written by Olʹga A. Ladyženskaja and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Harmonic Analysis And Partial Differential Equations
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Author : Anatoly Golberg
language : en
Publisher: Springer Nature
Release Date : 2023-04-26
Harmonic Analysis And Partial Differential Equations written by Anatoly Golberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-26 with Mathematics categories.
Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations
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Author : N. V. Krylov
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-09-07
Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations written by N. V. Krylov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-07 with Differential equations, Parabolic categories.
This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov–Safonov and the Evans–Krylov theorems, are taken from old sources, and the main results were obtained in the last few years. Presentation of these results is based on a generalization of the Fefferman–Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called “ersatz” existence theorems, saying that one can slightly modify “any” equation and get a “cut-off” equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.
Second Order Parabolic Differential Equations
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Author : Gary M. Lieberman
language : en
Publisher: World Scientific
Release Date : 1996
Second Order Parabolic Differential Equations written by Gary M. Lieberman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.
Boundary Value Problems Of Mathematical Physics
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Author : O. A. Ladyzhenskaya
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Boundary Value Problems Of Mathematical Physics written by O. A. Ladyzhenskaya and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Boundary value problems categories.
Singular Solutions Of Nonlinear Elliptic And Parabolic Equations
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Author : Alexander A. Kovalevsky
language : en
Publisher: ISSN
Release Date : 2016
Singular Solutions Of Nonlinear Elliptic And Parabolic Equations written by Alexander A. Kovalevsky and has been published by ISSN this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Differential equations, Elliptic categories.
This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography
Elliptic Hyperbolic And Mixed Complex Equations With Parabolic Degeneracy
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Author : Guo Chun Wen
language : en
Publisher: World Scientific
Release Date : 2008
Elliptic Hyperbolic And Mixed Complex Equations With Parabolic Degeneracy written by Guo Chun Wen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
In the recent half-century, many mathematicians have investigated various problems on several equations of mixed type and obtained interesting results, with important applications to gas dynamics. However, the Tricomi problem of general mixed type equations of second order with parabolic degeneracy has not been completely solved, particularly the Tricomi and Frankl problems for general Chaplygin equation in multiply connected domains posed by L Bers, and the existence, regularity of solutions of the above problems for mixed equations with non-smooth degenerate curve in several domains posed by J M Rassias. The method revealed in this book is unlike any other, in which the hyperbolic number and hyperbolic complex function in hyperbolic domains, and the complex number and complex function in elliptic domains are used. The corresponding problems for first order complex equations with singular coefficients are first discussed, and then the problems for second order complex equations are considered, where we pose the new partial derivative notations and complex analytic methods such that the forms of the above first order complex equations in hyperbolic and elliptic domains are wholly identical. In the meantime, the estimates of solutions for the above problems are obtained, hence many open problems including the above TricomiOCo Bers and TricomiOCoFranklOCoRassias problems can be solved. Sample Chapter(s). Chapter 1: Elliptic Complex Equations of First Order (247 KB). Contents: Elliptic Complex Equations of First Order; Elliptic Complex Equations of Second Order; Hyperbolic Complex Equations of First and Second Orders; First Order Complex Equations of Mixed Type; Second Order Linear Equations of Mixed Type; Second Order Quasilinear Equations of Mixed Type. Readership: Graduate students and academics in analysis, differential equations and applied mathematics.